Problem: Solve for $x$ and $y$ using substitution. ${x-3y = -7}$ ${y = -6x-4}$
Explanation: Since $y$ has already been solved for, substitute $-6x-4$ for $y$ in the first equation. ${x - 3}{(-6x-4)}{= -7}$ Simplify and solve for $x$ $x+18x + 12 = -7$ $19x+12 = -7$ $19x+12{-12} = -7{-12}$ $19x = -19$ $\dfrac{19x}{{19}} = \dfrac{-19}{{19}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = -6x-4}\thinspace$ to find $y$ ${y = -6}{(-1)}{ - 4}$ $y = 6 - 4$ $y = 2$ You can also plug ${x = -1}$ into $\thinspace {x-3y = -7}\thinspace$ and get the same answer for $y$ : ${(-1)}{ - 3y = -7}$ ${y = 2}$